This paper presents a comprehensive 4D dynamic model of a bottomhole assembly (BHA) used for directional drilling of oil and gas wells. Although directional drilling has been in practice for some time, it still poses several challenges, particularly related to building an autonomous drilling system. The difficulty with drilling automation derives from the complexity of the process that includes interaction with the borehole and fluid (mud) flow and complex downhole vibrations, such as bit-bounce (axial), whirl (lateral), and stick/slip (torsional). Moreover, the measurements from a limited number of downhole sensors are usually contaminated with high noise levels, and can only be transmitted at low rates with long transmission delays using mud pulsing, or at a high cost using wired pipe. Therefore, it is preferable that the directional drilling system work autonomously with limited communication to the surface. To facilitate this, a compressive physics-based model of the BHA behavior was created to be used in control system development.

In this work, the 4D dynamic model of the BHA accounts for the dynamics in rotation, axial motion, and bending along two lateral directions. The model uses a lumped mass-spring system and the system parameters (mass and stiffness) are derived from the shear beam theory of a flexible beam under certain boundary conditions.

Simulation results of the model were successful in qualitatively replicating the three types of downhole vibrations, namely bit-bounce, whirl, and stick/slip, and are discussed in this paper. The model is shown to qualitatively replicate downhole conditions and can be implemented in real-time, thereby making it suitable for autonomous directional drilling control.

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